Sticking with continuous time, it is instructive to consider the symmetries of the problem and apply the notion of group invariance. As argued by Jaynes [1]}, one must first identify all transformations that leave our state of knowledge unchanged. Consistency then requires that the prior probabilities be invariant under those transformations. For instance, if one's prior state of knowledge is oblivious to a spatial translation \(x \rightarrow x + c\) , then the prior distribution for \(x\)  should be uniform. If one's state of knowledge is instead invariant under a scale transformation \(x \rightarrow \lambda x\) , then the appropriate choice should be the Jeffreys prior, \(\rho (x) \sim 1/x\) .
